Geometrically nonlinear analysis of the stability of the stiffened plate taking into account the interaction of eigenforms of buckling

The aims of this work are a detailed consideration in a geometrically nonlinear formulation of the stages of the equilibrium behavior of a compressed stiffened plate, taking into account the interaction of the general form of buckling and local forms of wave formation in the plate or in the reinforcing ribs, comparison of the results of the semi-analytical solution of the system of nonlinear equations with the results of the numerical solution on the Patran-Nastran FEM complex of the problem of subcritical and postcritical equilibrium of a compressed stiffened plate. Methods. Geometrically-nonlinear analysis of displacement fields, deformations and stresses, calculation of eigenforms of buckling and construction of bifurcation solutions and solutions for equilibrium curves with limit points depending on the initial imperfections. An original method is proposed for determining critical states and obtaining bilateral estimates of critical loads at limiting points. Results. An algorithm for studying the equilibrium states of a stiffened plate near critical points is described in detail and illustrated by examples, using the first nonlinear (cubic terms) terms of the potential energy expansion, the coordinates of bifurcation points and limit points, as well as the corresponding values of critical loads. The curves of the critical load sensitivity are plotted depending on the value of the initial imperfections of the total deflection. Equilibrium curves with characteristic bifurcation points of local wave formation are constructed using a numerical solution. For the case of action of two initial imperfections, an algorithm is proposed for obtaining two-sided estimates of critical loads at limiting points.

RELIABILITY OF CORRODED STIFFENED PLATE SUBJECTED TO UNIAXIAL COMPRESSIVE LOADING

The work is focused on the reliability of corroded stiffened plates subjected to compressive uniaxial load based on the progressive collapse approach as stipulated by the Common Structural Rules for Bulk Carriers and Oil Tankers, employing the limit state design. Two different cases have been investigated. In the first model, the corrosion degradation led to uniform thickness loss, whereas the mechanical properties were unchanged, as given in the Rules. In the second model, the plate thickness degradation was followed by mechanical properties reduction. The uncertainties related to the mechanical properties, thicknesses, and initial imperfections of the corroded stiffened plate were taken into account. Several initial design solutions of stiffened plates, as well as different severity levels of corrosion degradation were investigated. The results show that structural reliability significantly decreases with corrosion development, especially when in addition to the initial imperfections and corrosion plate thickness reduction, corroded plate surface roughness and the changes in the mechanical properties were considered. The uncertainties, their origins and confidence levels are discussed. It was found that non-linear time-dependent corrosion degradation accounting not only for the thickness reduction due to corrosion wastage but also the subsequent decrease of mechanical properties lead to a significant reduction in the reliability index. Additionally, it was defined that the reliability estimate is very sensitive to the uncertainties related to the initial thickness and the spread of corrosion degradation as a function of the time. Incorporating the probability of corrosion detection into the original reliability model introduces additional information about the validity of structural degradation that may lead to a higher beta reliability index estimate compared to the original model.

ANALYTICAL AND EXPERIMENTAL INVESTIGATION ON THE FREE VIBRATION OF SUBMERGED STIFFENED STEEL PLATE

The approach developed in this paper applies to vibration analysis of rectangular stiffened plate coupled with fluid. It is obvious that the natural frequencies of a submerged structure are less than those of in vacuum and these are due to the effect of added mass of water to the structure. This paper focuses on the experimental, analytical and numerical solution of natural frequencies of submerged stiffened plate. The analytical solution based on the deflection equation of submerged orthotropic plate, Laplace’s equation and Rayleigh's method in vibration analysis. By used the FEM software the numerical results for natural frequencies are derived. The natural frequencies of the stiffened plate are obtained practically by using Fast Fourier Transformation functions (FFT) in experimental analysis. Experimental results demonstrate the validity of analytical and numerical solution and results.

FULL-SCALE MEASUREMENTS OF WELDING-INDUCED INITIAL DEFLECTIONS AND RESIDUAL STRESSES IN STEEL-STIFFENED PLATE STRUCTURES

Plated structures such as ships and offshore structures are constructed using welding techniques that attach support members (or stiffeners) to the plating. During this process, initial imperfections develop in the form of initial deformations (deflections or distortions) and residual stresses. These initial imperfections significantly affect the buckling and ultimate strength of these structures. Therefore, to assess the strength of welded plate structures, it is very important to predict the magnitude and pattern of welding-induced initial imperfections and their effects on buckling and ultimate strength. To determine the reliability of the prediction methods, it is desirable to validate the theoretical or numerical predictions of welding-induced initial imperfections through comparison with full-scale actual measurements. However, full-scale measurement databases are lacking, as they are costly to obtain. This study contributes to the development of a full-scale measurement database of welding-induced initial imperfections in steel-stiffened plate structures. The target structures are parts of real (full-scale) deckhouses in very large crude oil carrier class floating, production, storage and offloading unit structures. For parametric study purposes, four test structures by varying plate thickness are measured while the stiffener types and weld bead length are fixed. Modern technologies for measuring initial deformations and residual stresses are applied. The details of the measurement methods are documented for the use of other researchers and practicing engineers who welding-induced initial imperfections.

STRESS DISTRIBUTION IN THE HOLLOW STIFFENED HYBRID LAMINATED COMPOSITE PANELS IN SHIP STRUCTURES UNDER SINUSOIDAL LOADING

A simplified hollow stiffened hybrid laminated plate model has been developed for the marine structures. The detailed stress analysis through the thickness of the stiffened plate based on the higher order shear deformation theory has been carried out under sinusoidal loading. The hybrid laminates are made by wrapping the GFRP laminates with CFRP at the outermost layers of the stiffened panel. This hybridization technique can be an optimum solution from the point of view of cost reduction as well as enhancement of strength properties. The layer-wise stresses for the stiffened plate have been calculated in the present paper. A 3D polynomial curve fitting technique has been used to obtain higher accuracy and consistency in the computation of stresses. The computer code has been developed using MATLAB considering the plates as eight noded isoparametric plate bending element and the stiffener has been modeled as three noded isoparametric beam element. The stiffened panel has also been analysed using the ANSYS14.0 software package considering 2D model. The results obtained from the present formulation have been compared with those available in the published literature to validate the present formulation. The stiffened panels made of GFRP, CFRP and GFRP-CFRP hybrid laminates have been studied here. An extensive parametric study has been carried out with varying fibre content in the laminates.